\magnification = 2200 %\magstep3
%\vsize=1.05\vsize

\def\UseTimesRoman{
\font\cmr=Times
\font\TR=Times at 10pt
\font\TRXII=Times at 12pt
\font\TRXIV=Times at 14pt
\font\TRXX=Times at 20pt
\font\TRXXIV=Times at 24pt
\font\TI=TimesI at 10pt     %Times Italic
\font\TB=TimesB at 10pt     %Times Bold
\font\TBI=TimesBI at 10pt   %Times Bold Italic
\font\TBIviii=TimesBI at 8pt
\font\TBIv=TimesBI at 5pt
%\font\TO=TimesO at 10pt  %Times Oblique (Times Roman, slanted 22%
  %    with EdMetrics)
\font\TO=TimesI at 10pt  %Times Oblique (Times Roman, slanted 22% with EdMetrics)

\font\TIVIII=TimesI at 8pt
\font\TRVIII=Times at 8pt
\font\TIVI=TimesI at 6pt
\font\TRVI=Times at 6pt

	     \font\tenrmscld=Times at 10 pt
        \font\sevenrmscld=Times at 7 pt
        \font\fivermscld=Times at 5 pt

        \font\teniscld=cmmi10 at 10.3 pt
        \font\seveniscld=cmmi10 at 7.21 pt
        \font\fiveiscld=cmmi10 at 5.15 pt
        \font\tensyscld=cmsy10 at 10.3 pt
        \font\sevensyscld=cmsy10 at 7.21 pt
        \font\fivesyscld=cmsy10 at 5.15 pt
        \font\tenexscld=cmex10 at 10.3 pt
        \font\tenbfscld=cmbx10 at 10.3 pt
        \font\sevenbfscld=cmbx10 at 7.21 pt
        \font\fivebfscld=cmbx10 at 5.15 pt

\font\Courier = Courier
\font\Symbol = Symbol

\def\Omega{\hbox{{\Symbol W}}}

\textfont0=\tenrmscld \scriptfont0=\sevenrmscld\scriptscriptfont0=\fivermscld
\def\rm{\fam0\tenrmscld}
\textfont1=\teniscld \scriptfont1=\seveniscld \scriptscriptfont1=\fiveiscld
\def\mit{\fam1} \def\oldstyle{\fam1\teni}
\textfont2=\tensyscld \scriptfont2=\sevensyscld \scriptscriptfont2=\fivesyscld
\def\cal{\fam2}
\textfont3=\tenexscld \scriptfont3=\tenexscld \scriptscriptfont3=\tenexscld
\def\it{\TI}
\def\sl{\TO}
\def\bf{\TB}
\def\rm{\TR}
%\def\tt{\ttCourier}
\def\tt{\Courier}
\def\abstractfont{\TRVIII}
\def\footnotefont{\TRVIII}
\def\tinyfont{\TRvi}
\def\smalltitlefont{\TRXII}
\def\titlefont{\TRXIV}
\def\bigtitlefont{\TRXX}
\def\verybigtitlefont{\TRXXIV}
\textfont9=\TBI \scriptfont9=\TBIviii \scriptscriptfont9=\TBIv
\def\mbi{\fam9}
\rm
        }

%\UseTimesRoman

\def\BR{\Bbb R}             % Besondere Buchstaben
\def\BC{\Bbb C}
\def\BI{\Bbb I}
\def\BN{\Bbb N}
\def\BQ{\Bbb Q}
\def\BS{\Bbb S}
\def\BZ{\Bbb Z}
\def\Tilde{$_{\hbox{\cmrXX \~{}}}$}
\def\ST{\hbox{\eu T }}
\def\SRS{\hbox{\eu RS}}
\def\i{\hbox{{\bf i}}}

\font\sc=cmcsc10 at 10 pt   %% or: at 10 pt
\font\eu=eusb10 %at 10 pt
\font\small=cmr8 at 8 pt
\font\cmrX=cmbx10 scaled \magstep 1 %% 12 point CM
\font\cmrXX=cmbx12 scaled \magstep 1 %%

\hsize 7 true in
\vsize 9 true in
\hoffset = -0.20 true in
\voffset -0.25 true in
\parskip=3pt

\overfullrule = 0pt



\input amssym.def            % small letters for UNIX,  not: AMSsym.def
\input epsf.def% \input epsf %for UNIX
%\input epsf          %\input epsf.def for MAC f"ur BILDER!!
\input pics.tex

\input BoxedEPS
\SetTexturesEPSFSpecial
\HideDisplacementBoxes

\def\lf{\ \hfil\break}       % Neue Zeile ohne Einr"ucken, 'linefeed'
\def\cl{\centerline}
\def\Lf{\vskip1pt\noindent}   % Neue Zeile mit breiterem Zwischenraum
\def\LF{\medskip\noindent}   % Neue Zeile mit breiterem Zwischenraum
\def\R90{{\rm Rot}(90^\circ)}
\def\Dd#1{{\partial \over \partial #1}}

\nopagenumbers

\vglue -10pt
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%

\cl {\cmrX How Anaglyphs Work }

\lf
%\cl{\sc  Comment}
In the Action Menu of the Polyhedral Category one finds
{\bf Show Anaglyph Demo}. Selecting this starts up a graphic 
demonstration that attempts to explain pictorially the ideas  
behind the anaglyph stereo rendering of 3D objects.  One 
sees a diagram showing how the currently selected polyhedron 
is being projected from two different viewpoints (the left-eye and 
right-eye viewpoints). In more detail:
\Lf
{\it Step 1.}
Viewed through red-green glasses one sees:
\item{(i)} the current regular polyhedron in front of the screen, 
\item{(ii)} one projection center,
even further in front of the screen, and three projection rays,
\item{(iii)} the projection of the polyhedron onto the computer screen.

\noindent
If one takes the glasses off, then everything which appeared to be
in front of the screen is drawn twice, one copy in red, the other in
green. The projected polyhedron is drawn once in yellow. The
red-green glasses are filters, and the yellow color passes through
both of them, while the red color passes so poorly through the green
filter that it cannot be distinguished from the black background,
and similarly, the green color cannot be seen through the red
filter. 
\Lf
{\it Step 2.}
Now, with the red-green glasses on, press the {\it Right Arrow Key}.
The result is that a second projection center and the corresponding
 second projection is added to the 3D-image. Because the second
 projection is again colored yellow, one sees it as a second projection
 on the screen.  (Note that while {\it Mouse Rotation} of the polyhedron is
 enabled, the projection centers remain fixed.)
 \Lf
{\it Step 3.}
Finally, again with the red-green glasses on, press the {\it Left Arrow Key}.
While it is pressed, the colors of the two projected images get changed:
one turns red, the other green. Our brain interprets this immediately as
a three dimensional object. It is some sort of polyhedron, but looks rather
different from the projected one. If one moves ones eyes to the vicinity
of where the projection centers appear to be, then this distortion gets
less. Note that the original polyhedron now shows some distortion
because the red and green images were computed under the assumption
that the viewer looked orthogonally down onto the screen. -- Press and
release the  {\it Left Arrow Key} repeatedly! The impression is somewhat
stronger if one kicks the polyhedron with the mouse so that it keeps rotating.
\Lf
{\it Step 4.}
Other {\it Mouse Operations} are also enabled: \lf
By pressing SHIFT one can scale the whole image, including the projection
centers. \lf
By Pressing CONTROL one can move the polyhedron with the
mouse in the two directions parallel to the screen, with the projection 
centers remaining fixed. \lf
By Pressing SHIFT + OPTION one can move
the polyhedron vertically, to and from the screen (Mouse movement in
y-direction). One can thus study how the projected images change if
one changes the relative position of the polyhedron to the two projection
centers -- and how the shape of the object varies which our brain reconstructs
from the two changing projections.

\bye
 

 




